Electrode Surface Coverage with Deposit Generated Under Conditions of Electrochemical Nucleation and Growth. A Mathematical Analysis

Abstract

The theory of the diffusion limited electrochemical nucleation and growth of a deposit consisting of isolated 3D hemispherical nuclei has been re-analysed. The analysis focuses on a widely discussed model which assumes formation of “diffusion zones” around the growing nuclei. It has been proposed in the literature that the deposit-free fraction of the surface area of the substrate can be directly calculated from the substrate coverage with the “diffusion zones”. The aim of this work is to analyse whether such an approach can be applied for the growth of isolated 3D hemispherical nuclei. This is accomplished by evaluation of equations which describe nuclei radii at various stages of the deposition process. The formulae allow determining the substrate surface coverage with the growing deposit. This, in turn, allows simulating and analysing faradaic currents due to other than the electrodeposition reactions which take place at the deposit-free fraction of the substrate surface. Both instantaneous and progressive modes of the nucleation are discussed and the influence of the nucleation type on the faradaic currents is outlined. A comparison with other approaches reported in the literature indicates that the deposit-free fraction of the substrate surface may not always be determined by means of recalculation of the substrate coverage with the “diffusion zones”. Graphical abstract: [Figure not available: see fulltext.]